10.8 Analytical Method (Method B)

The goal of the analytical method, also referred to as Method B, is to provide an alternative technique to demonstrate or quantify the spectral compatibility of a technology with the basis systems. The result of this activity will be the determination of a deployment guideline of a loop transmission technology that would be considered to be spectrally compatible with the basis systems.

There could be numerous reasons for wanting to use the analytical method to determine spectral compatibility as opposed to using the method of signal power limitations, that is, via the SM classes. One reason could be that the technology to be deployed does not meet any of the nine SM classes defined earlier; the analytical method could be used to determine a deployment guideline for which this technology under test could be deployed and be spectrally compatible with the basis systems. Another reason could be that although the technology under test meets one or more of the spectrum management classes, the spectral characteristics of the technology could be such that the analytical method would allow a greater deployment guideline than that provided by the spectrum management classes.

One point to note is that although the analytical method does quantify the spectral compatibility of the technology under test with the basis systems, it does not quantify the spectral compatibility with other technologies in the cable that are not on the basis systems list. To assure performance of the new technology in the cable, crosstalk evaluations should be performed using crosstalk from each of the SM classes.

10.8.1 Determination of Spectral Compatibility with Basis Systems Using Method B

The analytical method requires that the spectral compatibility of the new technology (or technology under test) be evaluated for each of the basis systems. In other words, a spectral compatibility evaluation of some form needs to be done relative to each of the following basis systems:

Voice-grade services and technologies
Enhanced business services
DDS per T1.410
ISDN BRI per T1.601
HDSL
ADSL and RADSL technologies
HDSL2
2B1Q SDSL
In the second issue of T1.417, G.shdsl replaces 2B1Q SDSL on the basis systems list.

The general process for determining the spectral compatibility with each basis system is an iterative process that requires determining the performance target of the basis system based on a reference disturber, computing the performance of the basis system with disturbance from the new technology, and then comparing the results. In some cases the determination of spectral compatibility is done by evaluating relative margin and in other cases by evaluating absolute margin. Figure 10.15 shows a high-level crosstalk model for performance evaluation. In general, the following basic steps are performed in determining the spectral compatibility of a "new" technology with each basis system.

First, determine the target margin of the basis system at the target equivalent working length Z kft of 26-gauge wire. This target margin of the basis system is computed by applying a reference disturbance to the input of a basis system receiver operating on a loop with an EWL of Z.
Second, calculate the margin of the basis system operating on the same loop of EWL Z using crosstalk disturbance with the "new" technology and a mixture of disturbers, including the "new" technology.
If the new margin computed in step 2 is greater than the target margin from step 1 less some delta (i.e., target margin ”delta) specified for each basis system, then this new technology is spectrally compatible with the specific basis system at the working length Z. Depending on how much greater the margin is, it may be desirable to repeat steps 1 “3 using a longer EWL of Z'. As long as the computed "new" margin is greater than the target margin less the specified delta, then the new technology is spectrally compatible with the basis system at EWL of Z'.
If the new margin is less than the target margin less a specified delta, then the "new" technology is NOT spectrally compatible with the specific basis system at EWL of length Z. We must then reduce the EWL to a shorter length of Z' and repeat the computations of step 2. The loop lengths in the evaluations have a resolution of 500 ft. Keep reducing the EWL in 500 ft increments until a value of Z' meets the target margin less the specified delta determined in step (1).
Steps (1) through (4) are repeated for each of the basis systems and the resulting EWLs are recorded. Select the shortest Z' from all of the tests, and this is the resulting deployment guideline that will assure spectral compatibility with all of the basis systems.

Figure 10.15. System model for evaluating crosstalk disturbance into basis system.

graphics/10fig15.gif

NEXT and FEXT Models

As described in Chapter 9 on spectral compatibility, the near-end crosstalk model used in the analytical method is the simplified NEXT model of

where S ( f ) is the PSD of the interfering system, is coupling co-efficient for 49-NEXT disturbers, n is the number of NEXT disturbers, and f is the frequency in Hz. The far-end crosstalk model is defined as

graphics/10equ05.gif

where S ( f ) is the PSD of the interfering system, n is the number of FEXT disturbers, k = 8 x 10 ^-20 is the FEXT coupling coefficient for 49-FEXT disturbers, l is the channel length, and f is the frequency in Hz.

In some cases, the two-piece model is used for modeling next. The two-piece NEXT model is defined as

graphics/10equ06.gif

where f is frequency in Hz, S ( f ) is the power spectral density of the interfering system, and a ₁ b ₁ a ₂ b ₂ are constants defined in Table 10.16 corresponding to 1, 10, 24, and 49 disturbers. The two piece model is plotted in Figure 10.16.

Figure 10.16. Two-Piece NEXT.

graphics/10fig16.gif

Table 10.16. Constants for the Two-Piece NEXT Model

Number of Disturbers	a ₁	b ₁	a ₂	b ₂
1	6.598 x 10 ^-11	0.6	8.881 x 10 ^-15	1.5
10	7.071 x 10 ^-10	0.5	9.518 x 10 ^-14	1.4
24	1.925 x 10 ^-9	0.45	1.580 x 10 ^-13	1.4
49	4.782 x 10 ^-9	0.4	2.391 x 10 ^-13	1.4

Mixing Crosstalk

When a mixture of crosstalk is required in basis system compatibility evaluation, the FSAN (Full Service Access Network) method of combining crosstalk is used. Instead of adding directly the crosstalk power terms, each component term is raised to power of 1/0.6 and the resulting terms are added together. The final sum is then raised to the power of 0.6. This summing operation may be expressed as

where Xtalk ( f, n _i ) is either the NEXT or FEXT noise component, n _i is the number of disturbers of the i th noise component, and N is the total number of unlike disturber types.

Ideal DFE Equation for PAM-Based Systems

Computation of margin for DFE-based PAM systems, for which 2B1Q is a 4-level PAM system, is computed using the ideal DFE equation for PAM-based systems. Expressed in dB form, the ideal DFE equation for PAM-based systems is

where f _B is the symbol rate (or Baud rate) of the PAM-based system, SNR _req is the required SNR for the basis system, and f _SNR ( f ) is the folded receiver signal-to-noise ratio. The folded SNR for PAM-based systems is expressed as

where S(f) is the desired signal's transmit PSD, H(f) ² is the squared magnitude channel insertion gain, and N(f) is the total noise PSD seen at the receiver input.

Ideal DFE Equation for Single-carrier Based Systems

Computation of margin for DFE-based single-carrier systems, such as CAP or QAM, is computed using the ideal DFE equation for QAM-based systems. Expressed in dB form, the ideal DFE equation for QAM-based systems is

where f _B is the symbol rate (or Baud rate) of the single-carrier system, SNR _req is the required SNR for the basis system, and f _SNR ( f ) is the folded receiver signal-to-noise ratio. The folded SNR for QAM-based systems is expressed as

where S ( f ) is the desired signal's transmit PSD, H ( f ) ² is the squared magnitude channel insertion gain, and N ( f ) is the total noise PSD seen at the receiver input.

Computations for Multicarrier (DMT) Systems

Computation of margin for DMT systems may be done as follows . DMT is a multicarrier system that effectively divides the transmit spectrum into N evenly spaced tones with a carrier spacing of Df = 4.3125 kHz. Bits are allocated to each tone based on the Shannon capacity of the individual tone compensated for by the SNR gap. The capacity in bits/Hz at an individual carrier frequency f _i is given by

where SNR ( f _i ) is the signal-to-noise ratio at center tone frequency f _i and the SNR is expressed as

S ( f _i ) is the desired signal PSD at center tone frequency f _i , H ( f ) ² is the squared magnitude of the loop insertion gain, N ( f ) is the total noise that includes both crosstalk and background noise, and G is the signal-to-noise ratio gap expressed in dB and it is equal to 9.75 dB - (coding gain in dB) + (margin in dB).

The total capacity of the multicarrier system is computed by integrating the capacity across all of the tones. Because we are computing capacities of discrete tones, we simply add all of tone across the carrier frequencies. The reciprocal of the tone spacing is the DMT symbol interval T. The total bit capacity in the symbol interval is expressed as

and the total bit rate R (bit/sec) is computed by , where T is the DMT symbol interval in seconds, which is also equal to the reciprocal of spacing between the center tone frequencies.

To compute the margin of a DMT system, we first need to know the line bit rate that the DMT system will be operating. By knowing the bit rate, we can determine the capacity C (in bits/Hz) by C = R · T . A simple way to compute the margin of a DMT system is to average the signal-to-noise ratio across all of the active tones N by

and the margin expressed in dB ( g _m ) is computed by

where g _c is the coding gain expressed in dB.

The above computation methods are used for computing the spectral compatibility of a new technology with the basis systems. The following sections describe the conditions for spectral compatibility with each of the basis systems.

10.8.2 Voice Grade Services Spectral Compatibility

In general, voice grade services contain a family of technologies that utilize the frequency spectrum from 0 to approximately 4 kHz. Such services and technologies include speech signals, dual and single tone signaling, low frequency signaling, and digital and analog data. Performance of speech data is generally subjective in nature, and the SM standard does not provide any guidance for evaluating the subjective effects of crosstalk into speech signals. However, the performance of data services can be quantified . Hence, spectral compatibility of new technologies with voice grade services assume that a V.90 modem is the victim technology, since V.90 modems have the greatest sensitivity to noise than any other voice grade data signal. Spectral compatibility into V.90 systems is evaluated simply by computing the total crosstalk power in the 0 “4 kHz voice band and comparing it to set thresholds.

Evaluations into the voice band are done for both the upstream and downstream channels. In each case we assume 49-NEXT disturbers into the 0 “4 kHz frequency band. The 49-disturber NEXT coupling model used for this frequency band is

where f is frequency in Hz and is in the range from 200 “20,000 Hz. For voice grade services, there are two evaluations that need to be performed: (1) absolute values of the PSD in the range from 200 to 4000 Hz and (2) total NEXT noise in the 200 to 4000 Hz band.

First, the near-end crosstalk PSD resulting from the new technology disturbing signal must be less than or equal to -97.5 dBm/Hz at any frequency in the band from 200 to 4000 Hz. In other words, when we pass the new technology PSD through the above 49-NEXT coupling equation, all PSD values in the frequency band from 200 to 4000 Hz cannot exceed -97.5 dBm/Hz. Mathematically, this is expressed as

This criteria requires that the disturbing signal PSD be less than -29 dBm/Hz across the frequency band from 200 to 4000 Hz.

Second, the total NEXT noise in the 200 “4000 Hz band coming from 49-disturbers must be less than or equal to -75 dBm/Hz. Mathematically, this test is described as

where the PSD is expressed in linear units such as mW/Hz.

The above two criteria together defines a restriction in the total crosstalk power in the voice band while allowing for some variation in the PSD value at different frequencies in the band.

10.8.3 Enhanced Business Services Spectral Compatibility

Enhanced business services utilize the frequency band from 0 to 10 kHz, but the voice services supported under this umbrella utilize the same 0 “4 kHz band as those of conventional voice grade services. The primary difference with conventional voice grade services is that the enhanced business services support signaling functions that are modulated by an 8 kHz carrier. Therefore, spectral compatibility with enhanced business services must cover the signaling frequency band from 6 to 10 kHz while the lower frequencies are covered by the criteria for voice grade services.

As with conventional voice grade services, we use the techniques of evaluating absolute values of the PSD in the range from 6000 to 10,000 Hz for determining the spectral compatibility with enhanced business services.

The near-end crosstalk PSD resulting from the new technology disturbing signal must be less than or equal to -96 dBm/Hz at any frequency in the band from 6000 to 10,000 Hz. In other words, when we pass the new technology PSD through the above 49-NEXT coupling equation, all PSD values in the frequency band from 6000 to 10,000 Hz cannot exceed -96.0 dBm/Hz. Mathematically, this is expressed as

This criteria requires that the disturbing signal PSD be less than -29 dBm/Hz across the frequency band from 6000 to 10,000 Hz.

10.8.4 DDS per T1.410 Spectral Compatibility

The digital data system defined in T1.410 uses AMI technology for transmission of data signals from bit rates of 2.4 kb/s to 64 kb/s. The AMI signal uses a 50 percent duty cycle, which is similar to that of T1 service. The computation of the spectral compatibility with DDS is provided with the following method.

DDS Margin Computation

The transmit signal spectrum of AMI signal for DDS is defined as

graphics/10equ21.gif

where f _o is the signaling rate (or line bit rate) and K is a constant that is a function of the bit rate. Two bit rates are used for determining the spectral compatibility with DDS, namely, 9.6 kb/s and 64 kb/s. Note that for the 64 kb/s payload service, the line rate contains an additional 8 kb/s of overhead so the bit rate for evaluating spectral compatibility is 72 kb/s. For 9.6 kb/s, K = 1/(3,634,868) and for 64 kb/s (i.e., 72 kb/s line rate) K = 1/(6,848,000). The margin in dB of a DDS receiver is computed by

where SNR _folded is the folded SNR expressed as

and SNR _req is the required SNR of 17.3 dB for a 10 ^-7 bit error rate.

DDS Reference Crosstalk

Each bit rate of DDS has a specified evaluation loop for computing spectral compatibility. For 72 kb/s line rate, the evaluation loop is 13 kft of 26-gauge wire. For 9.6 kb/s, the evaluation loop is 27 kft of 26-gauge wire. To assess the affect of crosstalk onto DDS from a "new" technology, a relative comparison with 49-disturbers of ISDN basic rate crosstalk is made; in this case, the Spectrum Management Class 1 template represents the ISDN PSD. Hence, the reference crosstalk disturber into DDS is ISDN basic rate. If the new technology produces the same or higher margins than from ISDN, then the new technology is considered to be spectrally compatible with DDS.

Spectral Compatibility Criteria

To be considered spectrally compatible with DDS systems, the new technology must not produce any greater disturbance than that from 49-disturbers from SM Class 1 into DDS when computed under the following test conditions:

49 "new" technology NEXT and FEXT
24 spectrum management class 1 NEXT/FEXT + 24 new technology NEXT/FEXT

A background noise of -140 dBm/Hz should also be included. Evaluation must be done for both 9.6 kb/s and 64 kb/s payload conditions. As mentioned earlier, the required SNR for DDS is 17.3 dB, which is the operating point for a 10 ^-7 bit error rate. There is no delta value defined when evaluating spectral compatibility with DDS.

10.8.5 ISDN per T1.601 Spectral Compatibility

For ISDN, the spectral compatibility is computed using the ideal DFE equation for PAM-based systems. The evaluation loop should be either 17.5 kft of 26-gauge wire or the maximum length of 26-gauge wire that the technology is capable of operating, whichever is shorter. The reference crosstalk environment for ISDN is 49-NEXT from the SM Class 1 template. For this case, the two-piece NEXT model as defined above is used.

To be considered spectrally compatible with ISDN systems, the new technology must not produce any greater disturbance than that from 49-disturbers from SM Class 1 into ISDN when computed under the following test conditions:

49 "new" technology NEXT and FEXT
24 spectrum management class 1 NEXT/FEXT + 24 new technology NEXT/FEXT

A background noise of -140 dBm/Hz should also be included. This test basically says that no new technology shall introduce more crosstalk into ISDN than that from 49-self-NEXT ISDN disturbers.

10.8.6 HDSL Spectral Compatibility

For HDSL, the spectral compatibility is computed using the ideal DFE equation for PAM-based systems. The evaluation loop should be either 9 kft of 26-gauge wire or the maximum length of 26-gauge wire that the technology is capable of operating, whichever is shorter. The reference crosstalk environment for HDSL is 49-NEXT from the SM Class-3 template. This is effectively the same as 49-SNEXT HDSL disturbers. For this case, the simplified NEXT model is used.

To be considered spectrally compatible with HDSL systems, the new technology must not produce any greater disturbance than that from 49-disturbers from SM Class 3 into ISDN when computed under the following test conditions:

49 new technology NEXT and FEXT
24 SM Class 3 NEXT/FEXT + 24 new technology NEXT/FEXT

A background noise of -140 dBm/Hz should also be included. This test basically says that no new technology shall introduce more crosstalk into HDSL than that from 49-self-NEXT HDSL disturbers.

10.8.7 ADSL and RADSL Spectral Compatibility

ADSL used DMT technology; RADSL uses single-carrier (CAP) technology. Both systems use the same spectra for upstream and downstream transmission. Showing spectral compatibility with ADSL also assures spectral compatibility with RADSL. Spectral compatibility with ADSL can be evaluated using the method described above for DMT-based systems. For ADSL and RADSL, the simplified NEXT coupling model is used.

There are three performance levels required in demonstrating spectral compatibility with ADSL, namely:

4850 kb/s downstream and 645 kb/s upstream on a test loop of 9 kft of 26-gauge wire
3095 kb/s downstream and 415 kb/s upstream on a test loop of 11.5 kft of 26-gauge wire
425 kb/s downstream and 105 kb/s upstream on a test loop of 15.5 kgt of 26-gauge wire

The respective reference crosstalk talk environments for each of the above performance levels are defined as follows:

24 SM Class 3 template NEXT/FEXT disturbers
24 SM Class 2 template NEXT/FEXT disturbers
24 SM Class 1 template NEXT/FEXT disturbers

Margin is computed first for performance level A. If the tests for performance level A pass, then margin is computed for performance level B and so on. Spectral compatibility with ADSL is declared only when the new technology crosstalk gives greater than or equal to 6 dB of margin at the specified bit rate and loop length. If the performance level A tests fail, then the test is redone a new reference bit rate and a shorter loop length. The crosstalk and loop length environments for each of the upstream and downstream performance levels are provided as follows.

Loop Length (kft of 26-gauge wire)	Data Rate (kb/s)
9 < L 10	4595 + 255 x (10 - L)
10 < L 11.5	3095 + 1000 x (11.5 - L)

Loop Length (kft of 26-gauge wire)	Data Rate (kb/s)
11.5 < L 11.8	3095
11.8 < L 13.0	2045 + 875 x (13.0 - L)
13.0 < L 14.0	1265 + 780 x (14.0 - L)
14.0 < L 15.5	425 + 560 x (15.5 - L)

Downstream Performance Level A

Loop length L is 9kft of 26-gauge wire or less for a data rate of 4850 kb/s. The crosstalk conditions are

24 new technology NEXT and FEXT
12 spectrum management class 3 NEXT/FEXT + 12 new technology NEXT/FEXT

Loop Length (kft of 26-gauge wire)	Data Rate (kb/s)
L 6	950
6 < L 9	644 + 102 x (9 - L)